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Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift

Feng-yu Wang Orcid Logo

Journal of Differential Equations, Volume: 260, Issue: 3, Pages: 2792 - 2829

Swansea University Author: Feng-yu Wang Orcid Logo

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DOI (Published version): 10.1016/j.jde.2015.10.020

Abstract

Consider the stochastic evolution equation in a separable Hilbert space Hwith a nice multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the equation has a unique (possibly explosive) mild solution. Under a reasonable condition ensuring the non-explosion of t...

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Published in: Journal of Differential Equations
ISSN: 0022-0396
Published: Elsevier BV 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa28388
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first_indexed 2016-05-30T12:15:48Z
last_indexed 2021-01-07T03:44:48Z
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spelling 2021-01-06T14:49:12.3392602 v2 28388 2016-05-30 Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift 6734caa6d9a388bd3bd8eb0a1131d0de 0000-0003-0950-1672 Feng-yu Wang Feng-yu Wang true false 2016-05-30 SMA Consider the stochastic evolution equation in a separable Hilbert space Hwith a nice multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the equation has a unique (possibly explosive) mild solution. Under a reasonable condition ensuring the non-explosion of the solution, the strong Feller property of the associated Markov semigroup is proved. Gradient estimates and log-Harnack inequalities are derived for the associated semigroup under certain global conditions, which are new even in finite-dimensions. Journal Article Journal of Differential Equations 260 3 2792 2829 Elsevier BV 0022-0396 1 2 2016 2016-02-01 10.1016/j.jde.2015.10.020 http://dx.doi.org/10.1016/j.jde.2015.10.020 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2021-01-06T14:49:12.3392602 2016-05-30T04:38:43.2686640 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Feng-yu Wang 0000-0003-0950-1672 1
title Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
spellingShingle Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
Feng-yu Wang
title_short Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
title_full Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
title_fullStr Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
title_full_unstemmed Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
title_sort Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
author_id_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de
author_id_fullname_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de_***_Feng-yu Wang
author Feng-yu Wang
author2 Feng-yu Wang
format Journal article
container_title Journal of Differential Equations
container_volume 260
container_issue 3
container_start_page 2792
publishDate 2016
institution Swansea University
issn 0022-0396
doi_str_mv 10.1016/j.jde.2015.10.020
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://dx.doi.org/10.1016/j.jde.2015.10.020
document_store_str 0
active_str 0
description Consider the stochastic evolution equation in a separable Hilbert space Hwith a nice multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the equation has a unique (possibly explosive) mild solution. Under a reasonable condition ensuring the non-explosion of the solution, the strong Feller property of the associated Markov semigroup is proved. Gradient estimates and log-Harnack inequalities are derived for the associated semigroup under certain global conditions, which are new even in finite-dimensions.
published_date 2016-02-01T03:34:31Z
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score 11.013731

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